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Abstract:

A system that incorporates teachings of the present disclosure may
include, for example, an apparatus having a collimator having at least
one aperture and a fluorescence detector. The collimator can be
positioned next to a compound. The compound can emit fluorescence X-rays
when impacted by an X-ray beam generated by an X-ray source. The
collimator can absorb at least a first portion of the fluorescence X-rays
emitted by the compound and release at least a second portion of the
fluorescence X-rays at the at least one aperture. The second portion of
the fluorescence X-rays released by the at least one aperture have known
directional information based on a position of the collimator. The
fluorescence detector can detect the second portion of the fluorescence
X-rays released by the at least one aperture. A three-dimensional (3-D)
rendering of an elemental distribution of the compound can be determined
from the fluorescence X-rays detected and the directional information.
Additional embodiments are disclosed.

Claims:

1. An apparatus, comprising: a collimator positioned next to a compound,
wherein the collimator has at least one aperture, wherein the compound
emits fluorescence X-rays when impacted by an X-ray beam generated by an
X-ray source, wherein the collimator absorbs at least a first portion of
the fluorescence X-rays emitted by the compound and release at least a
second portion of the fluorescence X-rays at the at least one aperture,
and wherein the second portion of the fluorescence X-rays released by the
at least one aperture have known directional information based on a
position of the collimator; and a fluorescence detector for detecting the
second portion of the fluorescence X-rays released by the at least one
aperture, wherein a three-dimensional (3-D) rendering of an elemental
distribution of the compound is determined from the fluorescence X-rays
detected and the directional information.

2. The apparatus of claim 1, wherein the X-ray source is a synchrotron.

3. The apparatus of claim 1, wherein at least a portion of the at least
one aperture is covered with gold, tungsten, lead, depleted uranium, or
combinations thereof.

4. The apparatus of claim 1, wherein the at least one aperture comprises
one of a slit opening, a circular opening, a rectangular opening, and
concentric ring openings.

5. The apparatus of claim 1, wherein the fluorescence detector comprises
one of a charge coupled device detector, a complementary
metal-oxide-semiconductor detector, a double sided silicon strip
detector, and a silicon strip detector.

6. The apparatus of claim 1, comprising a controller adapted to: receive
detection data from the one or more fluorescence detectors; and determine
the 3-D rendering of the elemental distribution of the compound from the
detection data and the directional information associated with the
fluorescence X-rays emitted by the at least one aperture.

7. The apparatus of claim 6, wherein the controller is adapted to
determine from the detection data an energy of the fluorescence X-rays
emitted by the at least one aperture.

10. A method, comprising: receiving fluorescence X-rays responsive to an
X-ray beam impacting an object, wherein the fluorescence X-rays have
known directional information; measuring energy from the fluorescence
X-rays; and constructing a three-dimensional (3-D) rendering of an
elemental distribution of the object according to the measured energy of
the fluorescence X-rays and their corresponding directional information.

11. The method of claim 10, wherein the X-ray beam is generated by one of
a synchrotron X-ray source, and a non-synchrotron X-ray source.

12. The method of claim 10, wherein the fluorescence X-rays are released
by a plurality of apertures in each of a plurality of collimators
surrounding the object.

14. The method of claim 10, comprising detecting the fluorescence X-rays
with a plurality of fluorescence detectors surrounding a corresponding
plurality of collimators.

15. The method of claim 14, wherein each of the plurality of fluorescence
detectors comprises one of a charge coupled device detector, a
complementary metal-oxide-semiconductor detector, a double sided silicon
strip detector, and a silicon strip detector.

16. The method of claim 10, wherein the X-ray beam comprises one of a
thin slice X-ray beam, and an extended square X-ray beam.

17. A computer-readable storage medium, comprising computer instructions
to: measure energy from fluorescence X-rays emitted by a compound
impacted by an X-ray beam, wherein the fluorescence X-rays have known
directional information; and construct a three-dimensional (3-D)
rendering of an elemental distribution of the compound according to the
measured energy of the fluorescence X-rays and their corresponding
directional information.

18. The storage medium of claim 17, wherein the fluorescence X-rays are
released by a plurality of apertures in each of a plurality of
collimators surrounding the compound.

19. The storage medium of claim 17, comprising computer instructions to
measure the energy of the fluorescence X-rays from data supplied by a
plurality of fluorescence detectors surrounding a corresponding plurality
of collimators.

20. The storage medium of claim 19, wherein each of the plurality of
fluorescence detectors comprises one of a charge coupled device detector,
a complementary metal-oxide-semiconductor detector, a double sided
silicon strip detector, and a silicon strip detector.

Description:

PRIOR APPLICATION

[0001] The present application claims the benefit of priority to U.S.
Provisional Application No. 61/293,118 filed on Jan. 7, 2010, which is
hereby incorporated herein by reference.

FIELD OF THE DISCLOSURE

[0003] The present disclosure relates generally to a method and apparatus
for measuring properties of a compound.

BACKGROUND

[0004] Fluorescence X-ray techniques are widely used for elemental
analysis. It offers an excellent sensitivity to trace elements down to
picogram level. With the use of synchrotron X-ray sources, 3-D mapping of
trace elements inside volumetric samples can be obtained with the
so-called fluorescence X-ray computed tomography (XFCT) techniques
[1]-[10]. In most of XFCT studies, a pencil-beam of synchrotron X-rays
are used to scan through a volumetric sample from multiple view-angles,
as shown in FIG. 1.a. Fluorescence X-rays, originated from the subvolume
excited by the beam, are collected by a nonposition-sensitive x-ray
spectrometer. 3D distribution of trace elements can be reconstructed from
the measured line-integrals. As an alternative imaging scheme, confocal
geometry has also been explored by many authors.

[0005] Chukalina et al. have reported an analytical evaluation of XCFT
with a converging aperture system [11]. Woll et al. [12] and Vekemans et
al. [13] have reported the use of polycapillary x-ray optics for confocal
fluorescence x-ray microscopy. Similar to the line-by-line scanning
scheme, these methods rely on scanning the focal-spot point-by-point
through the volume (or surface)-of-interest to obtain a spatial mapping
of trace elements. Despite the excellent imaging performances
demonstrated in these studies, the need for mechanical scanning leads to
long imaging times. In recent years, many efforts have been dedicated to
improve the speed of XFCT studies [6], [7]. This is important for
potential in vivo imaging applications as those reported by Takeda et al.
[8]-[10]. The improved data acquisition speed allows for a greater
throughput for XFCT studies with a limited beam time, which could make
XFCT a more practical imaging modality for a wide range of applications.

[0008]FIG. 2 depicts an illustrative embodiment of the experimental setup
for the preliminary XFCT study. The detection system consists of an X-ray
CCD detector, a multiple pinhole aperture;

[0009] FIG. 3 depicts an illustrative embodiment of reconstructed phantom
images. The imaging mode, data acquisition time and beam configurations
are shown above each figure. Images were chosen to have the same variance
at the center. The 36 pinhole apertures were used for the ET-based
detection system;

[0010] FIG. 4. depicts an illustrative embodiment of the comparison
between the resolution-variance tradeoff curves achieved with the
ET-based approach and the line-by-line scanning approach. The curves are
chosen to be reasonably close to each other, indicating similar imaging
performances achieved with different approaches. The great reduction in
imaging time with the ET-based approach is demonstrated;

[0011] FIG. 5. depicts an illustrative embodiment of the energy spectrum
measured with the X-ray CCD detector. The energy threshold used for
selecting fluorescence components are shown in the figure;

[0012] FIG. 6. depicts an illustrative embodiment of the experimentally
acquired projections with fluorescence and Compton scattered x-rays. The
aperture used has 35 pinholes of 300 μm diameter. The projection data
was acquired by stepping a thin x-ray beam of 50 μm thickness through
the object. Data acquisition time was 5 minutes per slice;

[0015] FIG. 9 depicts an illustrative method according to the present
disclosure; and

[0016] FIG. 10 depicts an illustrative diagrammatic representation of a
machine in the form of a computer system within which a set of
instructions, when executed, may cause the machine to perform any one or
more of the methodologies disclosed herein.

DETAILED DESCRIPTION

[0017] One embodiment of the present disclosure entails an apparatus
having a collimator and a fluorescence detector. The collimator can be
positioned next to a compound. The collimator can have at least one
aperture. The aperture can be made of a thin sheet of heavy metal, such
as gold and tungsten, with openings machined through the metal sheet. The
compound emits fluorescence X-rays when impacted by an X-ray beam
generated by an X-ray source. The collimator in turn can absorb at least
a first portion of the fluorescence X-rays emitted by the compound and
allow a second portion of the fluorescence X-rays to pass through the
aperture to be detected by the fluorescence detector placed in proximity
to the aperture. A three-dimensional (3-D) rendering of an elemental
distribution of the compound can be determined from the fluorescence
X-rays detected and the directional information.

[0018] One embodiment of the present disclosure entails a method for
receiving fluorescence X-rays responsive to an X-ray beam impacting an
object, wherein the fluorescence X-rays have known directional
information, measuring energy from the fluorescence X-rays, and
constructing a three-dimensional (3-D) rendering of an elemental
distribution of the object according to the measured energy of the
fluorescence X-rays and their corresponding directional information.

[0019] One embodiment of the present disclosure entails a
computer-readable storage medium having computer instructions to measure
energy from fluorescence X-rays emitted by a compound impacted by an
X-ray beam, and to construct a three-dimensional rendering of an
elemental distribution of the compound according to the measured energy
of the fluorescence X-rays and their corresponding directional
information.

[0020] The present disclosure presents a feasibility study for using
detection systems similar to those commonly used in emission tomography
(ET) for X-ray fluorescence computer tomography (XFCT). The present
disclosure illustrates a detection system that combines high-resolution
semiconductor detectors with apertures that are made of heavy metal
sheets having arbitrary opening patterns. Possible opening patterns
include, but not limited to pinhole, multiple-pinhole, coded-aperture,
slit, or multiple-slit.

[0021] The key advantage of using an ET-based detection system is that 3-D
distributions of trace elements can be built up with much reduced
scanning time. In comparison to the conventional line-by-line scanning
scheme, the ET-based imaging system allows a great reduction in imaging
time, which has been one of the major hurdles for current XFCT studies.
In order to compare different imaging schemes for XFCT studies, an
analytical performance index was developed that is based on the
fundamental tradeoffs between image noise and spatial resolution
achievable with given detection configurations. To further demonstrate
the feasibility of using SPECT apertures for XFCT, a prototype
multiple-pinhole imaging system using a charge-coupled device (CCD)
detector was setup at the Advanced Photon Source (APS) for imaging
phantoms that contain solutions of several trace metals. Simultaneously
acquired 3-D distributions of these elements are presented.

[0022] The present disclosure illustrates an imaging scheme for XFCT
studies. With this scheme, the object is illuminated by a broad beam of
synchrotron x-rays. Fluorescence photons are collected by a specialized
emission tomography (ET) system that consists of multiple ultrahigh
resolution x-ray imaging-spectrometers, coupled to several
multiple-pinhole apertures. Two variations of this imaging scheme are
shown in FIGS. 1B and 1C. Unlike in the line-by-line scanning approach,
projections of the (fluorescence) x-ray-emitting object are acquired
simultaneously from multiple view-angles. It is therefore possible to
obtain a sufficient angular sampling using a much-reduced scanning
motion, or even with a stationary setup. This approach offers the
potential for a greatly improved imaging speed. In this research, Monte
Carlo and experimental approaches were used to verify the feasibility of
the ET-based approach for XFCT. The results are presented below.

[0023] In typical XFCT studies, the sample is scanned line-by-line with a
pencil-beam of synchrotron x-rays. Fluorescence photons emitted from the
narrow strip of volume illuminated by the beam are collected using a
none-position-sensitive x-ray spectrometer. The number of fluorescence
photons detected at a given beam position provides a line-integral of
x-ray emission from the thin stripe. Volumetric distribution of trace
elements can be reconstructed with either filtered backprojection (FBP)
or (penalized) maximum-likelihood (ML) algorithms previously developed
for various nuclear imaging modalities. The image formation process is
very similar to those for both single-photon emission computed tomography
(SPECT) with parallel-hole collimators and x-ray CT imaging with the
first generation geometry. The attenuations of both synchrotron x-rays
and fluorescence x-rays can be estimated based on the transmission CT
images acquired simultaneously with a second detector operated in the
standard x-ray CT mode, as previously discussed in [6][7].

[0024] The present disclosure proposes an alternative imaging scheme for
XFCT studies. Instead of using a pencil-beam of synchrotron x-rays, the
object is illuminated with two beam configurations as shown in FIGS. 1B
and 1C. With these approaches, the object is either scanned by a thin
slice or irradiated with a fixed broad beam of synchrotron x-rays. In
either cases, fluorescence x-rays emitted from the object are collected
by a detection system that consists of multiple x-ray
imaging-spectrometers coupled to multiple-pinhole apertures. The
detection system is very similar to that used for single photon emission
computed tomography (SPECT), except that a very high energy-resolution is
required to distinguish fluorescence x-rays emitted by different trace
metals and to separate fluorescence photons from Compton scattered
x-rays. 3-D distribution of trace-metals can be reconstructed from the
projection data acquired with the ET-based detection system.

[0025] In comparison to the line-by-line scanning scheme, the proposed
ET-based sampling method offers several attractive aspects. Firstly, with
Mode 2 and 3 geometries (shown in FIG. 1), the much-simplified scanning
motions would potentially lead to a much-reduced imaging time. Secondly,
with the line-by-line scanning, the angular sampling achieved is limited
by (a) the mechanical scanning procedures that can be practically
implemented and (b) the constraints on imaging time and dose delivery
during the measurement. In contrast, the multiple-pinhole based detection
system provides projections simultaneously from many view angles. This
can potentially be translated into an improved image quality. Thirdly,
with carefully designed Mode 2 geometries, it is possible to remove the
multiplexing in projection data. Therefore, the origin of each detected
x-ray is confined to a distinct voxel (or a small group of voxels) in the
object. In comparison to the use of Mode 1 and Mode 3 geometries, the
nonmultiplexing projections acquired with Mode 2 leads to reconstructed
images that are free of spatial correlation of imaging noise, as
typically seen in reconstructions with multiplexed data. This could offer
a superior image quality for objects that have extended distribution of
trace-elements.

[0026] There are three major concerns for the ET-based XFCT approach.
Firstly, high-resolution SPECT detection systems typically require the
use of collimation apertures that have very small open-fractions
(10-3-10-2). Compared to the line-by-line scanning geometry,
the ET-based approach uses a wider x-ray beam to illuminate a greater
portion of the object, which leads to a much stronger fluorescence signal
from the object. This partially compensates for the low detection
efficiency. Therefore, the key uncertainty is whether the use of ET-based
can provide an improved signal-to-noise ratio with comparable imaging
times. Secondly, Mode 2 and 3 tend to deliver a greater amount of
radiation dose per unit imaging time. Although radiation doses may not be
a serious issue for nonbiological samples, it does pose limitations for
potential in vivo studies [9][10].

[0027] Considering the reduced imaging time with Mode 2 and 3, it is
important to quantify how much radiation dose will be delivered per
imaging study. Thirdly, the spatial resolution provided by Mode 2 and 3
geometries is limited by the size of the pinholes. Given the constraints
on aperture fabrication and the considerations on detection efficiency,
the use of pinholes of less than 25 μm diameter is less practical.
Therefore, the spatial resolution offered by the ET-based detection
system is typically limited to several tens of microns to a few hundred
microns. In comparison, the line-by-line scanning scheme allows for a
spatial resolution at submicron level, although this would require a long
imaging time.

[0028] The concerns on radiation dose and imaging time may be mitigated by
the use of a synthetic imaging strategy. During an imaging study, the
entire object is first imaged with Mode 3 for a short period. This
provides a quick snapshot with a relatively low radiation dose. The image
obtained helps to define regions-of-interest (ROI) in the object. Once
the ROIs are defined, the beam profile is then modified to illuminate the
selected sub-volumes only with a thin slice of synchrotron x-rays (Mode
2). This provides high quality images of the ROIs with a fast imaging
time and a limited radiation dose delivered to a fraction of the sample
volume only.

[0029] For quantitative comparisons between different imaging modes, GEANT
4 [14] was used to model x-ray interactions and an analytical package
(developed in our previous studies [15]-[18]) to model the response of
the detection system for fluorescence x-rays emitted from the sample. For
a given object illumination scheme (line-by-line, slice-by-slice or whole
volume illumination), the system response function (SRF) is typically
represented by a matrix. Each of its elements gives the average number of
fluorescence photons that are originated from a given source voxel
containing a unit concentration of trace-element and detected on a given
detector element. In this study, most of interaction physics was
incorporated, such as photoelectric effect, Compton scattering, Rayleigh
scattering in the system model. The X-ray fluorescence process was
modeled using the low-energy physics (LEP) package (as part of GEANT4)
that was specially developed for the transport of low energy
electromagnetic radiation through matter. Polarization of synchrotron
x-rays was included in the study to account for the non-isotropic
distribution of Compton background.

[0030] To evaluate the line-by-line scanning approach (Mode 1 in FIG. 1),
two similar imaging configurations were included. The first one uses a
square beam of 100 μm×100 μm cross section to scan through
the object from 180 view angles, with an angular step size of 2 degrees.
At each angular position, the beam steps through the object in
64×64 equally spaced steps. The second configuration uses 200 μm
beam-width and 32×32 linear steps at each view angle. Fluorescence
x-rays are collected by a nonposition-sensitive spectrometer that has a
fixed detection efficiency of 20% for x-rays of 27-32 keV emitted from
any location in the object. The detector has an energy resolution of 250
eV that was modeled with Gaussian functions.

[0031] The ET-based detection system consists of a ring of six detectors.
The opposite detectors are positioned 2.4 cm apart. The simplified x-ray
detector consists of 256×256 square pixels of 55 μm×55
μm in size. The detector has a detection efficiency of 100% at 30 keV
and an energy resolution of 1.5 keV modeled with a Gaussian functions.
The depth-of-interaction effect was not modeled in the simulation. All
events detected were assumed to be full-energy event. A multiple pinhole
aperture is placed in front of each detector. The aperture was made of
pure gold of 250 μm thickness. Both the aperture-to-object-center
distance and the aperture-to-detector distance were 6 mm. In this study,
we examined two aperture configurations with 6×6 and 11×11
pinholes respectively. The distances between adjacent pinholes are 1.5 mm
and 0.8 mm for the two patterns. Note that the actual pinhole locations
are randomly shifted by an average of 0.1 mm from the designated grid
points in the square patterns. The pinhole diameter is 100 μm with
sharp knife-edge and acceptance cones of 45 degrees on both sides.

[0032] The object simulated is a cylinder of 6.4 mm diameter and 6.4 mm
long. It is filled with a uniform water solution of I-127 with a
concentration of 0.1 mg/g. Six groups of hot rods were also inserted for
comparing the imaging resolution achieved in reconstruction. The
diameters of hot-rods in each group are 1.25 mm, 1 mm, 0.75 mm, 0.5 mm,
0.3 mm and 0.2 mm respectively. Within each group, the minimum spacing
between centers of two adjacent holes is two times their diameter. In
this study, monochromatic x-rays of 35 keV were used to irradiate the
object and the x-ray beam has a fixed intensity of 106 per second
per mm2. Fluorescence x-rays of around 27 keV were selected with an
energy window of 2 keV in width.

[0033] To compare the imaging performances offered by different XFCT
imaging schemes, we used the modified Canner-Rao bound (MUCRB) as an
analytical performance index [19][20]. This approach is based on a simple
idea. In many cases, the user may have some ideas on the spatial
resolution functions that are required to fulfill an imaging task.
Therefore, a "good" imaging system could be chosen as the one that
delivers a resolution function similar to the target resolution function,
whilst having the lowest possible variance on a given pixel or the lowest
average variance across an arbitrarily selected cluster of pixels in the
image. This method is briefly described below.

[0034] For laying out the basic imaging problem, let's use x=[x1,
x2, . . . , xN]TεRN to denote the set of
unknown parameters, e.g., the concentrations of a given trace-element
across all the voxels in the object. The mapping from x to the projection
data y is governed by a conditional probability density function p(y;x).
For XFCT studies, y is a collection of random Poisson (or Gaussian)
variables that represent the measured numbers of fluorescence x-rays
detected on each detector element. The expectation of y is given by the
following transform

{tilde over (y)}=Ax+r, (1)

where A is the system-response matrix as described in Section II.D. r
denotes extra noise components. {circumflex over (x)}=[{circumflex over
(x)}1, {circumflex over (x)}2, . . . , {circumflex over
(x)}p]T is an estimator of the underlying distribution of a
trace metal in the sample, whose mean is

μ({circumflex over (x)})=Ex[{circumflex over
(x)}(y)]=∫{circumflex over (x)}(y)p(y;x)dy, (2)

where E[•] denotes the expectation operator.

[0035] The subsequent question is how to put a constraint on the spatial
resolution function delivered by a given imaging strategy? For an imaging
system, the spatial resolution function is typically represented by the
linearized local-impulse function (LIR) [21]. For the j'th voxel, it is
defined as

It is easily shown that lj and gj defined in (3) and (4) are
closely related. They become identical if the mean gradient matrix is
symmetric. Suppose that we know a priori the desired point-spread
function (or the mean gradient vector) at the j'th voxel is fj, we
can define a similarity measure

∥gj-fj∥C≦γ, (5)

where γ is a threshold that governs the degree of similarity
between fj and gj. C is a symmetric and positive definite
weighting matrix. ∥.∥ is the Euclidean norm of a
vector, so that

∥gj-fj∥C2=(gj-fj)TC-
(gj-fj). (6)

All estimators that satisfy constraint (5) with a small γ would
offer spatial resolution functions similar to the target f, regardless
the physical system configuration and the estimation method used.

[0036] It has been previously shown that for an imaging system/strategy to
deliver a spatial resolution satisfying (5), the minimum variance
attainable at a given pixel is bounded by [19], [20]

Var({circumflex over
(x)}j)≧fjT[J+(λC)-1]-1J[J+(λC-
)-1]-1fj. (7)

where λ is a scalar constant. The mean-gradient vector of the
efficient estimator that achieves this bound is given by

[0037] Note that the efficient estimator that (asymptotically). In this
study, we used (7) and (8) to evaluate the full-width-at-half-maximum
(FWHM) of the point-spread-function and the minimum variance attainable
at a given point j in the reconstructed image. By varying the target
resolution function f, one can obtain a curve representing the tradeoffs
between imaging resolution and pixel-wise variance. It was used as the
basis for comparing the different imaging schemes for XFCT studies.

[0038] The experimental setup used in this feasibility study is shown in
FIG. 2. The ET-based detection system consists of a single
front-illuminated X-ray CCD detector produced by Andor Technology (Model
# 934N). It has a detection area of 2.56 cm×1.52 cm, with
1280×768 square pixels of 20 μm×20 μm in size. The
detection efficiency of the detector is ˜80% at 5 keV, ˜30%
at 10 keV and ˜15% at 15 keV. The space around the CCD sensor was
filled with dry hydrogen and the sensor was cooled to -15° C. to
reduce dark noise. X-ray interactions were identified with a
photon-counting algorithm that was previously described in [16], [22].
This process offers an energy resolution of ˜250 keV FWHM. To
"simulate" the data acquisition process in Mode 3, the object is rotated
with 32 angular steps during a study as shown in FIG. 2B.

[0039] In this study, synchrotron x-rays of 15 keV were used to irradiate
the sample. The beam profile was modulated with a PC controlled aperture
that can provide both thin parallel beams (down to a few μm in width)
and extended beam with a maximum cross section of 5 mm×5 mm. The
beam intensity was fixed at ˜109 photons per second per
mm2. An x-ray shutter was installed on the beam line, whose
operation was synchronized with the readout of the CCD to eliminate the
smearing effect. In this study, the CCD was typically operated with 1-5
second accumulation time followed by a readout period of 1 s.

[0040] Two multiple-pinhole apertures were tested with the CCD detector.
The first one has 3×5 pinholes of 300 μm diameter and a pinhole
distance of 3 mm. The second aperture has 35 pinholes of 100 μm
diameter, arranged in a 5×7 array with 1.6 mm spacing between
adjacent pinholes. Both apertures were fabricated with tungsten sheets of
500 μm thickness. The pinholes have cone-shaped profiles on both
sides, with a fixed acceptance-angle of 45 degrees. The
detector-to-aperture distance was 1.5 mm and the center of the object is
1.2 mm from the aperture. The phantom used in this experimental study
consists of three plastic tubes of 0.75 mm inner diameter. These tubes
were filled with uniform solutions containing 0.1 μMole Fe, Zn and Br
respectively. A larger plastic tube was used to hold the three tubes
together. Its inner diameter is around 1.6 mm.

[0041] The performance benefit of ET-based XFCT approach over the
conventional line-by-line scanning approach is demonstrated in FIG. 3.
These images were chosen to have similar variances at the center. In this
study, the 36 pinhole aperture (216 pinholes with the entire system) was
used with the ET-based detection system. This configuration offers a
detection efficiency of 0.16% for fluorescence x-rays emitted from the
center of the object, which is a factor of 100 lower than that for the
detection system simulated in Mode 1 (20%). Despite the low detection
efficiency, both Mode 2 and 3 have delivered similar or better images
with much reduced imaging times. As previously discussed, using Mode 2
with carefully selected geometries (e.g. the detectors being very close
to the apertures), it is possible to eliminate the multiplexing in
projections. This leads to a superior imaging quality, with a
much-suppressed spatial correlation of image noise across the FOV.

[0042] For quantitative comparison, the resolution-variance tradeoff
curves achieved were plotted with the three data acquisition modes as
shown in FIG. 4. In this case, the ET-based detection system had a total
of 726 pinholes (11×11 pinholes per detector head), which provides
a detection efficiency of 0.8% for x-rays emitted from the center of the
object. When compared to the line-by-line approach, the ET-based
detection system allows one to reduce the imaging time by almost two
orders of magnitude. The radiation dose delivered to the object was
evaluated with GEANT 4 simulations and shown in FIG. 4. It is not
surprising that the use of a broad beam in Mode 3 leads to a
substantially increased radiation dose. For example, a 2-minute study
with the Mode 3 delivers 70 mGy dose to the object. It is almost 10 times
of the dose (8 mGy) delivered by a line-by-line study that lasts 180
minutes.

[0043] As previously discussed in Sec. MD, both radiation dose and imaging
time can be reduced by the use of a synthetic imaging strategy. If the
final imaging task is to map the distribution of a trace element within a
sub-volume only, one can start from a quick scan using Mode 3, followed
by a slice-by-slice scan in Mode 2 through the volume-of-interest only.
When compared to the conventional line-by-line scanning approach, the
synthetic imaging approach would allow high-speed XFCT studies with a
superior image quality and a much reduced radiation dose. This is evident
in the comparison shown in FIG. 4.

[0044] An energy spectrum measured with the CCD sensor is shown in FIG. 5.
The FWHM value around the Br photopeak was around 250 eV, which allows us
to resolve most of x-ray lines from the three trace elements. In the
first measurement, we used Mode 2 geometry and step the slice-beam in 50
μm through the object. The projections acquired with the CCD detector
coupled to the 15 pinhole aperture is shown in FIG. 6. The distribution
of Fe, Zn and Br inside individual slices illuminated by the beam were
reconstructed with the standard MLEM algorithm. A 3-D volumetric
distribution can be built up by stacking the reconstructed slices
together as shown in FIG. 7.

[0045] In the second measurement, the object is exposed to a broad beam of
synchrotron x-rays that was suppose to cover the entire object. The
object was rotated with 32 angles during the measurement, which takes
around 3 hours to complete. Unfortunately, the beam was mistakenly aimed
too high and missed the section containing most of the solutions.
Therefore, we were only able to resolve the Br peak and the Compton
components in the spectrum acquired. Using the projections with Br and
Compton scattered x-rays, 3-D images were reconstructed and shown in FIG.
8. Interestingly, with Compton scattered x-rays, we were able to
reconstructed the plastic tube structure, with some remnant Br
distribution seen inside one of the tubes.

[0046] In the present disclosure, the use of ET-based detection system for
XFCT studies were proposed and evaluated. Compared to the conventional
line-by-line scanning approach, the ET-based approaches allow for
tomographic imaging with a much-simplified scanning motion and
(potentially) offer a more complete angular sampling. In this study,
Monte Carlo simulations were used to compare the proposed approach with
the conventional line-by-line scanning approach. The feasibility of
ET-based approach for XFCT was also demonstrated with a prototype imaging
system installed at the GSECARS beam line at the Advanced Photon Source
(APS). Tomographic images were obtained based on both fluorescence and
Compton scatter x-rays.

[0047] Despite the relatively low detection efficiency, the use of the
ET-based system provides a substantially improved imaging speed (by 1 or
2 orders of magnitude) over that offered by the conventional line-by-line
scanning approach. This would greatly improve the throughput with limited
synchrotron beam time and therefore make XFCT a more practical imaging
modality for a wide range of applications. For dose-sensitive studies,
one can use the synthetic imaging strategy that combines XFCT studies
with different sampling geometry, tailored for the given object. This
could lead to XFCT studies with a fast data acquisition time, a
relatively low radiation dose to the object and an excellent imaging
quality.

[0048] The illustrative embodiments above can be implemented in part by a
computing system such as a computer, lap top, server, or mainframe
computer according to method 900 of FIG. 9. At step 902, a computing
system can measure energy from data supplied by a plurality of
fluorescent detectors that detect fluorescent X-rays emitted by a
compound impacted by an X-ray beam. The fluorescent X-rays have a known
directional information based on the position of the collimators, the
apertures, and the fluorescent detectors. At step 904, the computing
system can construct a three-dimensional rendering of an elemental
distribution of the compound determined from the measured energy of the
fluorescence X-rays and their corresponding directional information.

[0049] FIG. 10 depicts an exemplary diagrammatic representation of a
machine in the form of a computer system 1000 within which a set of
instructions, when executed, may cause the machine to perform any one or
more of the methods discussed above. In some embodiments, the machine may
be connected (e.g., using a network) to other machines. In a networked
deployment, the machine may operate in the capacity of a server or a
client user machine in server-client user network environment, or as a
peer machine in a peer-to-peer (or distributed) network environment.

[0050] The machine may comprise a server computer, a client user computer,
a personal computer (PC), a tablet PC, a smart phone, a laptop computer,
a desktop computer, a control system, a network router, switch or bridge,
or any machine capable of executing a set of instructions (sequential or
otherwise) that specify actions to be taken by that machine. It will be
understood that a communication device of the present disclosure includes
broadly any electronic device that provides voice, video or data
communication. Further, while a single machine is illustrated, the term
"machine" shall also be taken to include any collection of machines that
individually or jointly execute a set (or multiple sets) of instructions
to perform any one or more of the methods discussed herein.

[0051] The computer system 1000 may include a processor 1002 (e.g., a
central processing unit (CPU), a graphics processing unit (GPU, or both),
a main memory 1004 and a static memory 1006, which communicate with each
other via a bus 1008. The computer system 1000 may further include a
video display unit 1010 (e.g., a liquid crystal display (LCD), a flat
panel, or a solid state display. The computer system 1000 may include an
input device 1012 (e.g., a keyboard), a cursor control device 1014 (e.g.,
a mouse), a disk drive unit 1016, a signal generation device 1018 (e.g.,
a speaker or remote control) and a network interface device 1020.

[0052] The disk drive unit 1016 may include a tangible computer-readable
storage medium 1022 on which is stored one or more sets of instructions
(e.g., software 1024) embodying any one or more of the methods or
functions described herein, including those methods illustrated above.
The instructions 1024 may also reside, completely or at least partially,
within the main memory 1004, the static memory 1006, and/or within the
processor 1002 during execution thereof by the computer system 1000. The
main memory 1004 and the processor 1002 also may constitute tangible
computer-readable storage media.

[0053] Dedicated hardware implementations including, but not limited to,
application specific integrated circuits, programmable logic arrays and
other hardware devices can likewise be constructed to implement the
methods described herein. Applications that may include the apparatus and
systems of various embodiments broadly include a variety of electronic
and computer systems. Some embodiments implement functions in two or more
specific interconnected hardware modules or devices with related control
and data signals communicated between and through the modules, or as
portions of an application-specific integrated circuit. Thus, the example
system is applicable to software, firmware, and hardware implementations.

[0054] In accordance with various embodiments of the present disclosure,
the methods described herein are intended for operation as software
programs running on a computer processor. Furthermore, software
implementations can include, but not limited to, distributed processing
or component/object distributed processing, parallel processing, or
virtual machine processing can also be constructed to implement the
methods described herein.

[0055] While the tangible computer-readable storage medium 622 is shown in
an example embodiment to be a single medium, the term "tangible
computer-readable storage medium" should be taken to include a single
medium or multiple media (e.g., a centralized or distributed database,
and/or associated caches and servers) that store the one or more sets of
instructions. The term "tangible computer-readable storage medium" shall
also be taken to include any non-transitory medium that is capable of
storing or encoding a set of instructions for execution by the machine
and that cause the machine to perform any one or more of the methods of
the present disclosure.

[0056] The term "tangible computer-readable storage medium" shall
accordingly be taken to include, but not be limited to: solid-state
memories such as a memory card or other package that houses one or more
read-only (non-volatile) memories, random access memories, or other
re-writable (volatile) memories, a magneto-optical or optical medium such
as a disk or tape, or other tangible media which can be used to store
information. Accordingly, the disclosure is considered to include any one
or more of a tangible computer-readable storage medium, as listed herein
and including art-recognized equivalents and successor media, in which
the software implementations herein are stored.

[0057] Although the present specification describes components and
functions implemented in the embodiments with reference to particular
standards and protocols, the disclosure is not limited to such standards
and protocols. Each of the standards for Internet and other packet
switched network transmission (e.g., TCP/IP, UDP/IP, HTML, HTTP)
represent examples of the state of the art. Such standards are from
time-to-time superseded by faster or more efficient equivalents having
essentially the same functions. Wireless standards for device detection
(e.g., RFID), short-range communications (e.g., Bluetooth, WiFi, Zigbee),
and long-range communications (e.g., WiMAX, GSM, CDMA) are contemplated
for use by computer system 1000.

[0058] The illustrations of embodiments described herein are intended to
provide a general understanding of the structure of various embodiments,
and they are not intended to serve as a complete description of all the
elements and features of apparatus and systems that might make use of the
structures described herein. Many other embodiments will be apparent to
those of skill in the art upon reviewing the above description. Other
embodiments may be utilized and derived therefrom, such that structural
and logical substitutions and changes may be made without departing from
the scope of this disclosure. Figures are also merely representational
and may not be drawn to scale. Certain proportions thereof may be
exaggerated, while others may be minimized. Accordingly, the
specification and drawings are to be regarded in an illustrative rather
than a restrictive sense.

[0059] Although specific embodiments have been illustrated and described
herein, it should be appreciated that any arrangement calculated to
achieve the same purpose may be substituted for the specific embodiments
shown. This disclosure is intended to cover any and all adaptations or
variations of various embodiments. For example, FIG. 1D can provide a
fourth mode in which collimators can have multiple slit apertures.
Accordingly, combinations of the above embodiments, and other embodiments
not specifically described herein, will be apparent to those of skill in
the art upon reviewing the above description.

[0060] The Abstract of the Disclosure is provided with the understanding
that it will not be used to interpret or limit the scope or meaning of
the claims. In addition, in the foregoing Detailed Description, it can be
seen that various features are grouped together in a single embodiment
for the purpose of streamlining the disclosure. This method of disclosure
is not to be interpreted as reflecting an intention that the claimed
embodiments require more features than are expressly recited in each
claim. Rather, as the following claims reflect, inventive subject matter
lies in less than all features of a single disclosed embodiment. Thus the
following claims are hereby incorporated into the Detailed Description,
with each claim standing on its own as a separately claimed subject
matter.